import numpy as np
import matplotlib.pyplot as plt

def model(x,theta):
    return x.dot(theta)

def sigmoid(z):
    return 1/(1+np.exp(-z))

def cost(h,y):
    m=len(h)
    return -1/m*np.sum(y*np.log(h)+(1-y)*np.log(1-h))

def FP(x,theta1,theta2,theta3):
    a1=x
    z2=model(a1,theta1)
    a2=sigmoid(z2)
    z3=model(a2,theta2)
    a3=sigmoid(z3)
    z4=model(a3,theta3)
    a4=sigmoid(z4)
    return a2,a3,a4

def BP(x,y,theta1,theta2,theta3,a2,a3,a4,alpha):
    s4=a4-y
    s3=s4.dot(theta3.T)*(a3*(1-a3))
    s2=s3.dot(theta2.T)*(a2*(1-a2))

    m=len(x)
    dt3=1/m*a3.T.dot(s4)
    dt2=1/m*a2.T.dot(s3)
    dt1=1/m*x.T.dot(s2)

    theta3-=alpha*dt3
    theta2-=alpha*dt2
    theta1-=alpha*dt1

    return theta1,theta2,theta3

def grad(x,y,alpha=0.01,iter0=2000):
    m,n=x.shape
    theta1=np.random.randn(n,100)
    theta2=np.random.randn(100,100)
    theta3=np.random.randn(100,1)
    J=np.zeros(iter0)
    for i in range(iter0):
        a2, a3, a4=FP(x,theta1,theta2,theta3)
        J[i]=cost(a4,y)
        theta1, theta2, theta3=BP(x,y,theta1,theta2,theta3,a2,a3,a4,alpha)

    return theta1,theta2,theta3,a4,J

def score(h,y):
    return np.mean(y==[h>0.5])

if __name__ == '__main__':
    data=np.loadtxt('ex2data1.txt',delimiter=',')
    x=data[:,:-1]
    y=data[:,-1:]

    miu=np.mean(x,axis=0)
    sigma=np.std(x,axis=0)
    x=(x-miu)/sigma

    X=np.c_[np.ones(len(x)),x]

    np.random.seed(666)
    a=np.random.permutation(len(x))
    X=X[a]
    y=y[a]

    num=int(0.7*len(x))
    train_x,test_x=np.split(X,[num,])
    train_y,test_y=np.split(y,[num,])

    theta1, theta2, theta3, a4, J=grad(train_x,train_y)
    plt.plot(J)
    plt.show()

    print(score(a4,train_y))

    _,_,test_h=FP(test_x,theta1,theta2,theta3)
    print(score(test_h,test_y))